Dimension Reduction (DR) is the process of reducing a high dimension dataset with \(N\)  features into a dataset with \(p\)  features, where \(p \ll N\) .
Perhaps the most classic method in this domain is PCA[1]}, and a detailed study of PCA will illuminate many of the issues that arise when performing DR and DE with autoencoders. Unfortunately, most DR methods need an estimate of the number of latent variables as a user-defined input to the process of dimensionality reduction. Estimates of the number of latent variables in a particular dataset can come from a variety of principles (e.g., see Chapter 3 in [2]}) and looking at the example of PCA will provide illumination for our work.
